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Dirichlet Series and Dirichlet Polynomials
1996In this chapter we define the object of the investigation in our book: the Dirichlet series, the Riemann zeta-function and the Dirichlet L-functions. We also give some classical results concerning the behaviour of these series.
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UNIQUENESS THEOREMS FOR DIRICHLET SERIES
Bulletin of the Australian Mathematical Society, 2015We obtain uniqueness theorems for L-functions in the extended Selberg class when the functions share values in a finite set and share values weighted by multiplicities.
Wu, Ai-Di, Hu, Pei-Chu
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The Tribonacci Dirichlet series
Acta Mathematica Hungarica, 2023Tribonacci numbers \(T_n\) are the solutions of the 3rd order recurrence \[T_{n+3}=T_{n+2}+ T_{n+1} +T_{n}, \quad n\in \mathbb{N}, T_{1}=T_2=1, T_3=2. \;\;\;\;\; (1)\] As is well-known, they are generated by \[\sum_{n=0}^{\infty}T_nz^n=\frac{z}{1-z-z^2-z^3}\] and admit the explicit expression. As an analogue of the Fibonacci zeta-function \[\sum_{n=1}^{
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Probabilistic Methods for Dirichlet Series
2013The title of this chapter is a little emphatic, because the probabilistic methods will here concentrate essentially about one maximal inequality, which is fairly well-known in harmonic analysis, but will have a specific aspect, due to the Bohr point of view on Dirichlet series.
Hervé Queffélec, Martine Queffélec
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Hardy Spaces of Dirichlet Series
2013The forthcoming spaces \( {{\mathcal{H}}^{p}} \) of Dirichlet series (1 ≤ p ≤ ∞), analogous to the familiar Hardy spaces H p on the unit disk, have been successfully introduced to study completeness problems in Hilbert spaces ([63]), first for p = 2, ∞. Later on, the general case was considered in [10] for the study of composition operators.
Hervé Queffélec, Martine Queffélec
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Dirichlet Series with Trigonometric Coefficients
2021See the abstract in the attached pdf.
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General Properties of Dirichlet Series
2013For a real number θ, we denote by ℂ θ the following vertical half-plane: $${\mathbb{C}_\theta } = \left\{ {s \in \mathbb{C};\Re es > \theta } \right\}$$ .
Hervé Queffélec, Martine Queffélec
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Composition Theorems on Dirichlet Series
Canadian Mathematical Bulletin, 1963When two uniform functions , are given, each with a finite radius of absolute convergence R1 R2 respectively, and {λn}, {μν} are real positive increasing sequences tending to infinity, a theorem due to Eggleston [1], which is a generalisation of Hurwitz1 s composition theorem, gives information about the position of the singularities of a composition ...
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